On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

نویسندگان

  • M. Giorgetti
  • M. Rossi
  • M. Sala
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on the girth of tanner (3,7) quasi-cyclic ldpc codes

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Efficient encoding for a family of quasi-cyclic LDPC codes

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BCRI preprint On a class of quasi-cyclic LDPC codes

Abstract. We study a class of quasi-cyclic LDPC codes. We provide both a Gröbner basis approach, which leads to precise conditions on the code dimension, and a graph theoretic prospective, that lets us guarantee high girth in their Tanner graph. Experimentally, the codes we propose perform no worse than random LDPC codes with their same parameters, which is a significant achievement for algebra...

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Computation of Grobner Basis for Systematic Encoding of Generalized Quasi-Cyclic Codes

Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the systematic encoding of GQC codes is equivalent to the division algorithm in the theory of Gröbner basis of modules, there has been no algorithm that computes G...

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Quasi-cyclic LDPC codes with high girth

The LDPC codes are codes that approach optimal decoding performances, with an acceptable decoding computational cost ([1, 2, 3]). In this paper we present a class of quasi-cyclic LDPC codes and we show that we are able to guarantee some relevant properties of the codes. Experimentally, their decoding performance is comparable with the performance obtained by random LDPC codes. Traditionally, co...

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عنوان ژورنال

دوره 31  شماره No. 2

صفحات  13- 32

تاریخ انتشار 2011-01-22

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